In a large mixing bowl, combine all-purpose flour, sugar, and salt. In a separate bowl, gently warm the whole milk and mix in active dry yeast until dissolved. Pour the yeast mixture into the flour blend, then add eggs and melted butter. Knead the dough on a floured surface for about 10 minutes until smooth and elastic, then let it rise in a warm area for 1 hour, or until doubled in size.

In a medium saucepan, whisk together egg yolks, white sugar, whole milk, cornstarch, and vanilla extract. Cook over medium heat, stirring constantly until the mixture thickens and bubbles (about 5-7 minutes). Remove from heat and stir in butter until melted. Allow the filling to cool slightly, then incorporate whipped heavy cream until light and fluffy. Refrigerate until ready to use.

Once the dough has risen, punch it down to release air. On a floured surface, roll out the dough to about ½ inch thick. Use a donut cutter to stamp out the shapes, placing each onto a parchment-lined baking sheet. Cover with a clean kitchen towel and let them rise again for about 30 minutes until puffy and airy.

Heat vegetable oil in a deep fryer or large pot to 350°F (175°C). Carefully fry the donuts in batches, about 2-3 minutes per side, until they achieve a golden-brown color. Use a slotted spoon to transfer them to a plate lined with paper towels to drain excess oil.

Once the donuts have cooled slightly, use a pastry bag or a small spoon to fill each donut with the chilled Bavarian cream filling. Roll them gently in white sugar to create a sweet, sparkling finish before placing them on a serving plate.